You do have to go through security again. It is a normal security screening, however depending on when you are flying, DCA is generally a little less busy of an airport, and the concourses are really not very far and security is generally pretty well run. I think you'll be fine. it'll be a bit close but it's definitely makeable providing that your plane is on time.

That last one though is a big if. I don't know that stats, but I've never really thought of DCA as the most on-time airport.